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On the effects of microbubbles on Taylor–Green vortex flow

Published online by Cambridge University Press:  23 January 2007

ANTONINO FERRANTE  and
SAID E. ELGHOBASHI
ANTONINO FERRANTE
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
SAID E. ELGHOBASHI
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA 92697, USA
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Abstract

The paper describes a numerical study of the effects of microbubbles on the vorticity dynamics in a Taylor–Green vortex flow (TGV) using the two-fluid approach. The results show that bubbles with a volume fraction ∼10−2 enhance the decay rate of the vorticity at the centre of the vortex. Analysis of the vorticity equation of the bubble-laden flow shows that the local positive velocity divergence of the fluid velocity, ∇·U, created in the vortex core by bubble clustering, is responsible for the vorticity decay. At the centre of the vortex, the vorticity ωc(t) decreases nearly linearly with the bubble concentration Cm(t). Similarly, the enstrophy in the core of the vortex, ω2(t), decays nearly linearly with C2(t). The approximate mean-enstrophy equation shows that bubble accumulation in the high-enstrophy core regions produces a positive correlation between ω2 and ∇·U, which enhances the decay rate of the mean enstrophy.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 572 , February 2007 , pp. 145 - 177
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Auton, T. R. 1987 The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199–218.CrossRefGoogle Scholar
Detsch, R. M. 1991 Small air bubbles in reagent grade water and seawater 1. Rise velocities of 20 to 1000-μm-diameter bubbles. J. Geophys. Res. 96 (C5), 8901–8906.CrossRefGoogle Scholar
Djeridi, H., Gabillet, C. & Billard, J. Y. 2004 Two-phase Couette–Taylor flow: arrangement of the dispersed phase and effects on the flow structures. Phys. Fluids 16 (1), 128–139.CrossRefGoogle Scholar
Drew, D. A. 1983 Mathematical modeling of two-phase flow. Annu. Rev. Fluid Mech. 15, 261–291.CrossRefGoogle Scholar
Drew, D. A. & Passman, S. L. 1999 Theory of Multicomponent Fluids. Springer.CrossRefGoogle Scholar
Druzhinin, O. A. & Elghobashi, S. 1998 Direct numerical simulation of bubble-laden turbulent flows using the two fluid formulation. Phys. Fluids 10 (3), 685–697.CrossRefGoogle Scholar
Druzhinin, O. A. & Elghobashi, S. E. 2001 Direct numerical simulation of a three-dimensional spatially developing bubble-laden mixing layer with two-way coupling. J. Fluid Mech. 429, 23–61.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2003 On the physical mechanism of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15 (2), 315–329.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2004 On the physical mechanisms of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles. J. Fluid Mech. 503, 345–355.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2005 Reynolds number effect on drag reduction in a microbubble-laden spatially developing turbulent boundary layer. J. Fluid Mech. 543, 93–106.CrossRefGoogle Scholar
Gerz, T., Schumann, U. & Elghobashi, S. 1989 Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech. 200, 563–594.CrossRefGoogle Scholar
Hirsch, C. 1990 Numerical Computation of Internal and External Flows, vol. 2. John Wiley & Sons.Google Scholar
Marchioro, M., Tanksley, M. & Prosperetti, A. 1999 Mixture pressure and stress in disperse two-phase flow. Intl J. Multiphase Flow 25, 1395–1429.CrossRefGoogle Scholar
Maxey, M. R. 1987a The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.CrossRefGoogle Scholar
Maxey, M. R. 1987b The motion of small spherical particles in a cellular flow field. Phys. Fluids 30 (7), 1915–1928.CrossRefGoogle Scholar
Maxey, M. R. & Riley, J. 1983 Equation of motion for a small rigid sphere in a turbulent fluid flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
Mazzitelli, I. M., Lohse, D. & Toschi, F. 2003 On the relevance of the lift force in bubbly turbulence. J. Fluid Mech. 488, 283–313.CrossRefGoogle Scholar
Najm, H. N., Wyckoff, P. S. & Knio, O. M. 1998 A semi-implicit numerical scheme for reacting flow i. stiff chemistry. J. Comput. Physics 143 (2), 381–402.CrossRefGoogle Scholar
Prosperetti, A. & Zhang, D. Z. 1995 Finite-particle-size effects in disperse tho phase flows. Theoret. and Comput. Fluid Dynamics 7, 429–440.CrossRefGoogle Scholar
Rightley, P. M. & Lasheras, J. C. 2000 Bubble dispersion and interphase coupling in a free-shear flow. J. Fluid Mech. 412, 21–59.CrossRefGoogle Scholar
Roe, P. L. 1985 Some contributions to the modelling of discontinuous flows. In Proc. 1983 AMS-SIAM Summer Seminar on Large Scale Computing in Fluid Mechanics, Lectures in Applied Mathemathics, vol. 22, pp. 163–193. SIAM, Philadelphia.Google Scholar
Ruetsch, G. & Meiburg, E. 1993 On the motion of small spherical bubbles in two-dimensional vortical flows. Phys. Fluids A 5 (10), 2326–2341.CrossRefGoogle Scholar
Saffman, P. G. 1965 The lift on a small sphere in a slow shear flow. J. Fluid Mech. 22, 385–400. Corrigendum P. G. Saffman J. Fluid Mech. 31, p. 624, 1968.CrossRefGoogle Scholar
Schmidt, H., Schumann, U. & Volkert, H. 1984 Three dimensional, direct and vectorized elliptic solvers for various boundary conditions. Rep. 84-15. DFVLR-Mitt.Google Scholar
Sirignano, W. A. 2005 Volume averaging for the analysis of turbulent spray flows. Intl J. Multiphase Flow 31, 675–705.CrossRefGoogle Scholar
Sridhar, G. & Katz, J. 1999 Effect of entrained bubbles on the structure of vortex rings. J. Fluid Mech. 397, 171–202.Google Scholar
Taylor, G. I. 1923 On the decay of vortices in a viscous fluid. Philos. Mag. 46, 671–674.CrossRefGoogle Scholar
Van Leer, B. 1979 Towards the ultimate conservative difference scheme. v. a second order sequel to Godunov's method. J. Comput. Phys. 32, 101–136.CrossRefGoogle Scholar
Wang, L. P. & Maxey, M. R. 1993 The motion of microbubbles in a forced isotropic and homoheneous turbulence. Appl. Sci. Res. 51, 291–296.Google Scholar
Zhang, D. Z. & Prosperetti, A. 1997 Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions. Intl J. Multiphase Flow 23, 425–453.CrossRefGoogle Scholar